Consider the number 7,123,456.
a. Approximate the number by rounding to the nearest million.

This statement is false.

Every real matrix has real eigenvalues or comes in pairs of complex conjugate eigenvalues.

In general, the eigenvalues of a 2x2 matrix A can be found by solving the characteristic equation det(A - lambda*I) = 0, where I is the 2x2 identity matrix and lambda is the eigenvalue. The characteristic equation is a quadratic equation in lambda, and its solutions are the eigenvalues of A.

For a real 2x2 matrix, the coefficients of the characteristic equation are real, and so the solutions to the characteristic equation are either real or complex conjugate pairs. This follows from the fact that complex roots of real polynomials always come in complex conjugate pairs.

Now, suppose that a real 2x2 matrix A has eigenvalues i and 2i. Since these eigenvalues are not real, they must be complex conjugates of each other. That is, 2i is also an eigenvalue of A, and the other eigenvalue must be the complex conjugate of i, which is -i.

However, the characteristic equation of a 2x2 matrix with eigenvalues i and 2i is given by:

det(A - lambda*I) = (a - lambda)(d - lambda) - bc = (a - lambda)(d - lambda) - b*c

where A = [[a,b],[c,d]], and lambda = i or 2i.

If we substitute lambda = i into the above equation, we get:

(a - i)(d - i) - b*c = 0

Expanding this equation, we get:

ad - ai - di + i^2 - bc = 0

Simplifying, we get:

(ad - bc) - i(a + d) = 0

Since the matrix A has real entries, the imaginary part of this equation must be zero, which implies that a + d = 0. But this contradicts the assumption that A has eigenvalues i and 2i, since the sum of the eigenvalues of A is equal to the trace of A, which is a + d. Therefore, there cannot exist a real 2x2 matrix with eigenvalues i and 2i.

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Answer:

\(0.64*y = 40\)

Step-by-step explanation:

Answer:

64/100=40/y

Step-by-step explanation:

We use the simple equation of finding percentages, which would be the percentage (64) over 100 percent, as this is our total. If 64 percent of y equals 40, then the equation is 64/100=40/y. To solve for y, multiply 100 x 40= 4000, then divide by 64 to get the answer. Y=62.5

The ratio of students who wish they had x-ray vision to all students is 1:6.

The ratio of students who wish for flight to all students is 2:9.

The ratio of students who wish for flight to those who wish for invisibility is 2:3.

Find the total number of students who made a choice:

8 + 10 + 6 + 12 = 36

To find the ratio of students who wish they had x-ray vision to all students, we can write the ratio as:

x-ray vision : all students = 6 : 36

Simplifying this ratio by dividing both terms by 6 gives:

x-ray vision : all students = 1 : 6

Therefore, the ratio of students who wish they had x-ray vision to all students is 1 : 6.

To find the ratio of students who wish for flight to all students, we can write the ratio as:

flight : all students = 8 : 36

Simplifying this ratio by dividing both terms by 4 gives:

flight : all students = 2 : 9

Therefore, the ratio of students who wish for flight to all students is 2 : 9.

To find the ratio of students who wish for flight to those who wish for invisibility, we can write the ratio as:

flight : invisibility = 8 : 12

Simplifying this ratio by dividing both terms by 4 gives:

flight : invisibility = 2 : 3

Therefore, the ratio of students who wish for flight to those who wish for invisibility is 2 : 3.

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--The question is incomplete, answering to the question below--

"The table shows the type of super power that 36 students wish they had. each student could only pick one super power.

super power     students

flight                   8  

super strength  10  

x-ray vision        6

invisibility           12  

match the following ratios to what they describe.

description                                                                                                 ratio

The ratio of students who wish they had x-ray vision to all students   2:3

The ratio of students who wish for flight to all students                        1:6

The ratio of students who wish for flight to those who wish for invisibility 2 : 9"

The transformation that was not done to f(x) to obtain g(x) is a reflection.

To get the capability g(x) = - 4(x - 2) - 9 from the straight parent capability f(x) = x, the accompanying changes were applied:

In the horizontal direction: The parent capability f(x) = x has been moved 2 units to one side to become f(x - 2), which compares to the term (x - 2).

Vertical pressure: A factor of four has been used to vertically compress the function -f(x - 2) -4(f(x - 2)) is how this looks like.

Vertical rewriting: To become -4(f(x - 2)) - 9, which is equivalent to g(x), the function -4(f(x - 2)) has been shifted down by nine units.

Accordingly, every one of the changes referenced above have been applied to the straight parent capability f(x) = x to get g(x) = - 4(x - 2) - 9.

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The slope of the line that passes through (1, 1)  and (7, 5) is 2/3

From the question, the points are given as

a. (1, 1) and (7,5)

Rewrite the above points properly

So, we have the following ordered pairs

(1, 1) and (7,5)

The slope of the line is then calculated using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where

(x, y) = (1, 1) and (7,5)

Substitute the known values in the above equation

So, we have the following equation

Slope = (5 - 1)/(7 - 1)

Evaluate

Slope = 2/3

Hence, the slope of the line is 2/3

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Possible question

Find the slope of the line that passes through a. (1, 1) and (7,5)

The partial derivative diffusivity equation for spherical flow is ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t, and for hemispherical flow, it is the same equation.

1. The partial derivative diffusivity equation for spherical flow is derived from the spherical coordinate system and applies to radial flow in a spherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

2. The partial derivative diffusivity equation for hemispherical flow is derived from the hemispherical coordinate system and applies to radial flow in a hemispherical geometry. It can be expressed as ∂²p/∂r² + (1/r) ∂p/∂r = ϕμC/k ∂p/∂t.

1. For the derivation of the partial derivative diffusivity equation for spherical flow, we consider a spherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the polar angle (φ). By assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in spherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

2. Similarly, for the derivation of the partial derivative diffusivity equation for hemispherical flow, we consider a hemispherical coordinate system with the radial direction (r), the azimuthal angle (θ), and the elevation angle (ε). Again, assuming steady-state flow and neglecting the other coordinate directions, we focus on radial flow. Applying the Laplace operator (∇²) in hemispherical coordinates, we obtain ∇²p = (1/r²) (∂/∂r) (r² ∂p/∂r). Simplifying this expression, we arrive at ∂²p/∂r² + (1/r) ∂p/∂r.

In both cases, the term ϕμC/k ∂p/∂t represents the source or sink term, where ϕ is the porosity, μ is the fluid viscosity, C is the compressibility, k is the permeability, and ∂p/∂t is the change in pressure over time.

These equations are commonly used in fluid mechanics and petroleum engineering to describe radial flow behavior in spherical and hemispherical geometries, respectively.

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Given

The ordered pair (1, 4) is a solution to the equation x + y = 5 because 1 + 4 = 5 is a true statement. Which of the following ordered pairs is also a solution to the equation x + y = 5

Solution

The final answer

Answer:

27\(a^{9}\)\(b^3\\\)

Step-by-step explanation:

This is what happens

\((3)^{3} or (3^1)^{3}\)= \(3^{1x3}\) = \(3^{3}\) = 27

\((a^{3})^{3}\)= \(ax^{3x3}\) \(a^{9}\)

\((b)^{3}\)= \(b^{1x3}\) =\(b^{3}\)

The relationship between the two confidence intervals B) The width of I81 will be 1/3 the width of I9.

When constructing 99 percent confidence intervals to estimate the difference in means of two populations, r, and w, the width of the confidence intervals depends on the sample size used.

The width of a confidence interval is inversely proportional to the square root of the sample size. Since the sample size of I81 (81) is 9 times larger than the sample size of I9 (9), the width of I81 will be smaller than the width of I9.

To determine the relationship between the widths, take the square root of the ratio of the sample sizes:

√(81/9) = √(9) = 3

Thus, the width of I81 will be 1/3 the width of I9. The width of I81 will be 1/3 the width of I9. This is because when the sample size increases, the confidence interval becomes narrower, providing a more precise estimate of the difference in means between the two populations. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

two 99 percent confidence intervals will be constructed to estimate the difference in means of two populations, r and w. one confidence interval, i9 , will be constructed using samples of size 9 from each of r and w, and the other confidence interval, i81 , will be constructed using samples of size 81 from each of r and w. when all other things remain the same, which of the following describes the relationship between the two confidence intervals?

A) The width of I81 will be 1/9 the width of I9

B) The width of I81 will be 1/3 the width of I9

C) The width of I81 will be equal to the width of I9

D) The width of I81 will be 3 times the width of I9

E) The width of I81 will be 9 times the width of I9

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Answer:

The numbers on this ruler represent centimeters. 1.70cm

What is the precision of this ruler?

What is the greatest possible error for the measurement indicated by the arrow?

What is the margin of error for the measurement based on where the arrow is pointing on the ruler?

Step-by-step explanation:

The required solutions are,

0.1 cm is the precision of this ruler
0.05 cm is the greatest possible error for the measurement indicated by the arrow.
1.65 cm to 1.75 cm is the margin of error for the measurement based on where the arrow is pointing on the ruler

A ruler is a mathematical tool, used to measure the lengths of objects.
Rulers are calibrated into various units of measurement such as meters, centimeters, and milimeters, etc.

Here,
A scale is given for 10cm measurements and an arrow is pointed over 1.70 cm on the ruler,

0.1 cm is the precision of this ruler because every line on the ruler is 0.1 cm of measurement.
0.05 cm is the greatest possible error for the measurement indicated by the arrow.
1.65 cm to 1.75 cm is the margin of error, because the error could arise to the nearest point on the ruler, for the measurement based on where the arrow is pointing on the ruler,

Thus, solutions for the given problem are described above.

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Answer:

y = 1100 - 115x

Step-by-step explanation:

Let the monthly payment be $p

In two months Zach would have paid 2p dollars

Balance would be  1100 - 2p = y

We know after 2 months, balance y was actually 870

Substituting y = 870 we get
1100 - 2p = 870

Subtract 1100 on both sides

1100 - 1100 - 2p = 870 -1100

==> -2p = - 230

Divide by -2 on both sides

-2p/-2 = -230/-2

p = 115 which represents the monthly payment .

So the balance y after m months is given by the equation
y = 1100 - 115x

We can verify by plugging in the values for the second scenario
For 6 months
y = 1100 - 115 x 6 = 1100 - 690 = $410 which agrees with the given value so our equation is consistent

The possible coordinates of the point​ A is (-3, -5) and  (-3, 7)

The given parameters are:

This means that

A = (-3, y)

The distance between any two points is calculated as

D = √[(x₁ - x₂)² + (y₁ - y₂)²]

Substitute the known values in the above equation

So, we have

10 = √[(-3 - 5)² + (y - 1)²]

Evaluate the difference

10 = √[(-8)² + (y - 1)²]

Take the square of both sides

100 = (-8)² + (y - 1)²

So, we have

100 = 64 + (y - 1)²

Evaluate the like terms

(y - 1)² = 36

Take the square roots

y - 1 = ±6

This gives

y = 1 ± 6

So, we have

y = -5 and 7

Hence, the coordinates of point​ A is (-3, -5) and  (-3, 7)

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Answer: It is b

Step-by-step explanation:

Answer: 126.5

Step-by-step explanation:

This is Pythagoras theorem so a² + b² = c²

c² is always the diagonal bit

The soccer field is rectangle and draw the route of the players on and you get the triangle

a = 120

b = 40

c² = a² + b² (square root after)

120² + 40² = 16000

Then square root that to get 126.5

I hoped this helped so please thank and rate :)

Answer: 45

Step-by-step explanation: 9*5=45

Step-by-step explanation:

hope it helps you........

The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658.

The probability of an event occurring is defined by probability.

Probability is also called chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.

As per the given,

Total songs = 53

Like songs = 14

Probability of selecting and liking the first song = 14/53

Now since repetition is not allowed and one like the song has been chosen out of 14 thus, the remaining songs = 13, and total songs = 43 - 1 = 52

Probability of selecting liking the second song = 13/52

Probability of selecting liking the third song = 12/51

Probability of selecting liking the fourth song = 11/50

a)

The probability of liking all songs will be 14/53 x 13/52 x 12/51 x 11/50 = 0.03418.

b)

The probability of not liking the next four songs =1 - The probability of liking all songs

The probability of not liking the next four songs = 1 - 0.03418 = 0.96582.

Hence "The probability that all four songs are liked will be 0.03418 and the probability of not liking the next four songs will be 0.99658".

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The answer is true. The goal of a hypothesis test is indeed to demonstrate that the patterns observed in the sample data are not simply due to chance or sampling error, but rather represent real patterns in the population.

Hypothesis testing is a statistical tool used to determine whether a hypothesis about a population parameter is supported by sample data. The hypothesis being tested is called the null hypothesis, which assumes that there is no significant difference or relationship between variables in the population. The alternative hypothesis, on the other hand, suggests that there is a significant difference or relationship.

Through hypothesis testing, we can determine whether the observed differences or relationships in the sample are likely to occur by chance or are actually reflective of the true population. If the p-value (the probability of obtaining a result as extreme as the one observed, assuming the null hypothesis is true) is less than a predetermined level of significance, typically 0.05, we reject the null hypothesis and conclude that the alternative hypothesis is supported by the data.

In summary, the goal of a hypothesis test is to provide evidence that the observed patterns in the sample data are reflective of the true population and not just due to chance or sampling error.

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Answer:

Step-by-step explanation:

This is an isosceles triangle because 2 of the sides are the same length (marked with single slashed through them). The Isosceles Triangle Theorem tells that if 2 sides are congruent to each other, then the angles opposite those sides are congruent to each other as well. That means that the bottom left angle measures 68. According to the Triangle Angle-Sum Theorem, all the angles of a triangle have to add up to equal 180, so:

x = 180 - 68 - 68 so

x = 44

Answer:

a, c

Step-by-step explanation:

Let's start with one of each choice. That'll be 3 * 4 * 3 * 3 * 10 = 1080 pizzas. As for the second one, this time the toppings won't be 10 it will be 10 * 9 * 8 because we have 10, and then 9, and then 8 topping choices. This gives us 1080 * 9 * 8 = 77,760. Hope this helps!

Answer:

Step-by-step explanation:

Well, we can multiply the choices that they gave us, which is 3 by 4 by 3 by 3 by 10, which will give 1080 for the first part. Now, if you was to do only 3 toppings, it should be 3 by 4 by 3 by 3 by 3, which would give us 324. I don't know if this is right but I think this is the right answer.

Answer:

Total profit after 10 years = \(\$5,277,064\)

Step-by-step explanation:

Let \(a_n\)  represent the profit in the nth year

Then \(a_{n+1}\)  represents the profit in year  \(n+\)1

\(\text{Common ratio } r = \dfrac{a_{n+1}}{a_n}\)

The sum of a geometric sequence is given by
\(S_n = a_1 \cdot \dfrac{1 - r^n}{1-r}\)

where
\(a_1 =\) first term
\(r =\) common ratio
\(n =\) number of terms

Calculation of r

To calculate r we see that the profit increases by 16% every year

16% = 16/100 = 0.16

If profit increases by 0.16, then next year's profit
= this year's profit(1 + 0.16)

= this year's profit x 1.16

r = 1.16 the ratio of a term to the previous term

In this problem we are given the first term as
\(a_1 = 247,500\) \(\text{ = profit in first year}\)
\(n = 10 =\) number of years

\(r = 1.16\)

Plugging these values into equation [1] for the sum we get
\(\begin{aligned}S_n &= a_1 \cdot \dfrac{1 - r^n}{1-r}\\\\&= 247500 \cdot \dfrac{1-1.16^{10}}{1-1.16}\\\\& = 247500 \cdot \dfrac{-3.41143}{-0.16}\\& = 247500 \cdot 21.3215\\& = 5277064\end{aligned}\)

Therefore the total profit after 10 years
= $5,277,064

The solution set representing the number of cans each guest must bring to meet the goal is {5}.

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The required inverse of the given function is expressed as \(y=\sqrt{\frac{x+10}{7} }\)

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input.

Replacing y with x

x = 7y² – 10

Making y the subject of the formula:

7y² = x+ 10

Dividing both sides by 7

7y²/7 = (x+10)/ 7

y² = (x+10)/ 7

Taking the square root of both sides

\(\sqrt{y^{2} } =\sqrt{\frac{x+10}{7} }\)

\(y=\sqrt{\frac{x+10}{7} }\)

Hence the required inverse of the given function is expressed as  \(y=\sqrt{\frac{x+10}{7} }\)

Complete question:

Which equation is the inverse of y = 7x² – 10

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Answer:

$190

Step-by-step explanation:

My knowledge!

Hope it helps!

Answer:

190

Step-by-step explanation:

Step 1 find total amount of money she has saved

To do this simply multiply the amount of money she saves per week ( 4.75 ) by the number of weeks ( 8 )

Hence money she has saved = 8 * 4.75 = 35

Step 2 subtract cost of camera by amount of money she has saved

228 - 38 = 190

So we can conclude that she needs 190 more dollars to purchase the camera.

Answer: 351

Step-by-step explanation:

1/2 of the triangular prism is 3*6.5*9=175 and we have two prisms so therefore we multiply by 2 and get 351 meters.

Answer:

Step-by-step explanation:

V= Bh      where B=area of Base          h=height of shape

                                                               h=9

B= 1/2 bh    this h is h of the triangle base, different then h above

B= 1/2 (5)(6.5)

B=16.25

V=Bh

V= 16.25*9

V=146.25 in³

The piece of gum is stuck to the rear wheel. Then the minimum height is 8ft and the maximum height is 8ft from the ground.

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

A rider is riding a bicycle on a 6-foot wall at a rate of 1 foot per second.

The wheels have a radius of 1 foot, and a piece of gum becomes stuck to the rear wheel as shown, continuing to travel with the bicycle.

Then the diameter of the rear wheel is 2 ft.

A rider is riding a bicycle on a 6-foot wall, therefore the height of the lowest point of the rear wheel is 6 ft from the ground. And the highest point of the rear wheel is (6 + 2 = ) 8 ft.

If the piece of gum is stuck to the rear wheel, hence the minimum height is 8ft and the maximum height is 8ft from the ground.

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Answer:

minimum 6ft, max 8 ft

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Took the test